Foundational models of computation often abstract away physical hardware limitations. However, in extreme environments like In-Network Computing (INC), these limitations become inviolable laws, creating an acute trilemma among communication efficiency, bounded memory, and robust scalability. Prevailing distributed paradigms, while powerful in their intended domains, were not designed for this stringent regime and thus face fundamental challenges. This paper demonstrates that resolving this trilemma requires a shift in perspective - from seeking engineering trade-offs to deriving solutions from logical necessity. We establish a rigorous axiomatic system that formalizes these physical constraints and prove that for the broad class of computations admitting an idempotent merge operator, there exists a unique, optimal paradigm. Any system satisfying these axioms must converge to a single normal form: Self-Describing Parallel Flows (SDPF), a purely data-centric model where stateless executors process flows that carry their own control logic. We further prove this unique paradigm is convergent, Turing-complete, and minimal. In the same way that the CAP theorem established a boundary for what is impossible in distributed state management, our work provides a constructive dual: a uniqueness theorem that reveals what is \textit{inevitable} for distributed computation flows under physical law.

翻译：基础计算模型通常抽象掉物理硬件的限制。然而，在网内计算（INC）等极端环境中，这些限制成为不可违反的定律，在通信效率、有界内存和鲁棒可扩展性之间形成了一个尖锐的三难困境。主流的分布式范式虽然在其目标领域内功能强大，但并非为这种严格体制设计，因此面临根本性挑战。本文证明，解决这一三难困境需要视角的转变——从寻求工程权衡转向从逻辑必然性推导解决方案。我们建立了一个严格的公理化系统来形式化这些物理约束，并证明对于允许幂等合并算子的广泛计算类别，存在一个唯一的、最优的范式。任何满足这些公理的系统都必须收敛到单一的正规形式：自描述并行流（SDPF），这是一种纯粹以数据为中心的模型，其中无状态执行器处理携带自身控制逻辑的流。我们进一步证明这一唯一范式是收敛的、图灵完备的且是最小的。正如CAP定理为分布式状态管理中的不可能性划定了边界，我们的工作提供了一个建设性的对偶：一个唯一性定理，揭示了物理定律下分布式计算流的\textit{必然性}。